US9928314B2ActiveUtilityA1
Fitting sample points with an isovalue surface
Est. expiryApr 10, 2034(~7.7 yrs left)· nominal 20-yr term from priority
Inventors:David Leo Bonner
G06T 17/00G06F 17/175G06F 30/17G06F 17/10G06T 2210/56G06T 2215/06G06T 15/08G06T 2215/16G06F 30/00G06F 30/23G06F 17/5086G06F 17/50G06F 17/5018
61
PatentIndex Score
1
Cited by
48
References
13
Claims
Abstract
The invention notably relates to a computer-implemented method for designing a three-dimensional modeled object that represents a physical entity. The method comprises providing sample points; determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors; and fitting the sample points with an isovalue surface of the volumetric function, wherein the program further penalizes oscillations of the fitted isovalue surface.
Claims
exact text as granted — not AI-modifiedThe invention claimed is:
1. A computer-implemented method for generating a three-dimensional modeled object that represents a physical entity, comprising:
providing sample points;
determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors, wherein the distance from the explored orientation vectors involves a difference between a gradient of an argument volumetric function and an explored orientation vector at the sample points;
fitting the sample points with an isovalue surface of the volumetric function, wherein the optimization program further penalizes oscillations of the isovalue surface; and
displaying the three-dimensional modeled object generated based on the fitting.
2. The method of claim 1 , wherein the oscillations for an explored volumetric function involve a volume integral of a positive function of a derivation of the explored volumetric function.
3. The method of claim 2 , wherein the positive function is a square function.
4. The method of claim 2 , wherein the derivation of the explored volumetric function is a normalization of the explored volumetric function obtained by subtracting an average value of the volumetric function at the sample points.
5. The method of claim 4 , wherein the optimization program is: F
F
*
(
p
)
=
f
(
argmax
θ
,
ϕ
∫
∫
∫
V
f
(
θ
,
ϕ
,
p
)
nor
2
d
ν
,
p
)
where:
p={p 1 . . . p N } are the sample points,
F is the predetermined class of volumetric functions, defined on volume domain V, and
f
(
θ
,
ϕ
,
p
)
nor
=
f
(
θ
,
ϕ
,
p
)
-
∑
i
f
θ
,
ϕ
(
p
i
)
N
is the normalization of the explored volumetric function ƒ(θ, φ, p)=argmin ƒϵF Σ i ∥∇ƒ(p i )−n θ i φ i ∥, wherein N={n θ i φ i . . . n θ N φ N } are explored orientation vectors defined at the sample points P by azimuth and elevation angles θ={θ 1 . . . θ N } and φ={φ 1 . . . φ N }.
6. The method of claim 1 , wherein the sample points correspond to 3D curves sketched by a user and the optimization program explores the orientation vectors under a constraint that the explored orientation vectors be normal to the 3D curves and respect a minimal rotation propagation condition over each 3D curve.
7. The method of claim 6 , wherein the constraint that the explored orientation vectors respect the minimal rotation propagation condition corresponds to an application of a double reflection method.
8. The method of claim 6 , wherein the determining comprises solving the optimization program by a meta-heuristic optimization.
9. The method of claim 8 , wherein the meta-heuristic optimization is a particle swarm optimization.
10. The method of claim 9 , wherein the distance from the explored orientation vectors involves a sum of norms of the difference between the gradient of the argument volumetric function and the explored orientation vector at the sample points.
11. The method of claim 1 , wherein the physical entity is a manufacturing product.
12. A non-transitory data storage medium having recorded thereon a computer program that comprises instructions for performing a method of generating a three-dimensional modeled object that represents a physical entity, wherein the method comprises:
providing sample points;
determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors, wherein the distance from the explored orientation vectors involves a difference between a gradient of an argument volumetric function and an explored orientation vector at the sample points;
fitting the sample points with an isovalue surface of the volumetric function, wherein the computer program further penalizes oscillations of the isovalue surface; and
displaying the three-dimensional modeled object generated based on the fitting.
13. A system comprising a processor coupled to a memory and a graphical user interface, the memory having recorded thereon a computer program that comprises instructions for performing a method of generating a three-dimensional modeled object that represents a physical entity, wherein the method comprises:
providing sample points;
determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points, wherein the optimization program penalizes a distance from the explored orientation vectors, wherein the distance from the explored orientation vectors involves a difference between a gradient of an argument volumetric function and an explored orientation vector at the sample points;
fitting the sample points with an isovalue surface of the volumetric function, wherein the computer program further penalizes oscillations of the isovalue surface; and
displaying the three-dimensional modeled object generated based on the fitting.Join the waitlist — get patent alerts
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